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Simplifying r2 + 2r + -85 = -3 Reorder the terms: -85 + 2r + r2 = -3 Solving -85 + 2r + r2 = -3 Solving for variable 'r'. Reorder the terms: -85 + 3 + 2r + r2 = -3 + 3 Combine like terms: -85 + 3 = -82 -82 + 2r + r2 = -3 + 3 Combine like terms: -3 + 3 = 0 -82 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 2r + 82 + r2 = 0 + 82 Reorder the terms: -82 + 82 + 2r + r2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 2r + r2 = 0 + 82 2r + r2 = 0 + 82 Combine like terms: 0 + 82 = 82 2r + r2 = 82 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 82 + 1 Reorder the terms: 1 + 2r + r2 = 82 + 1 Combine like terms: 82 + 1 = 83 1 + 2r + r2 = 83 Factor a perfect square on the left side: (r + 1)(r + 1) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (r + 1) equal to 9.110433579 and -9.110433579.Subproblem 1
r + 1 = 9.110433579 Simplifying r + 1 = 9.110433579 Reorder the terms: 1 + r = 9.110433579 Solving 1 + r = 9.110433579 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 9.110433579 + -1 Combine like terms: 1 + -1 = 0 0 + r = 9.110433579 + -1 r = 9.110433579 + -1 Combine like terms: 9.110433579 + -1 = 8.110433579 r = 8.110433579 Simplifying r = 8.110433579Subproblem 2
r + 1 = -9.110433579 Simplifying r + 1 = -9.110433579 Reorder the terms: 1 + r = -9.110433579 Solving 1 + r = -9.110433579 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -9.110433579 + -1 Combine like terms: 1 + -1 = 0 0 + r = -9.110433579 + -1 r = -9.110433579 + -1 Combine like terms: -9.110433579 + -1 = -10.110433579 r = -10.110433579 Simplifying r = -10.110433579Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.110433579, -10.110433579}
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